Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem

DOI10.1063/1.1990120zbMath1110.81114arXivquant-ph/0505180OpenAlexW3105230785MaRDI QIDQ3438576

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Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0505180

Mathematics Subject Classification ID

Partitions of sets (05A18) Bell and Stirling numbers (11B73) Enumeration in graph theory (05C30) Quantum optics (81V80) Coherent states (81R30) Miscellaneous applications of number theory (11Z05) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (14)

\((p, q)\)-analogues of the generalized Touchard polynomials and Stirling numbers ⋮ Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers ⋮ A Faà di Bruno subalgebra of the graded dual of word symmetric functions ⋮ A simple combinatorial interpretation of certain generalized Bell and Stirling numbers ⋮ Walks, partitions, and normal ordering ⋮ Generalized Stirling numbers and hyper-sums of powers of binomials coefficients ⋮ Boson operator ordering identities from generalized Stirling and Eulerian numbers ⋮ Combinatorially interpreting generalized Stirling numbers ⋮ Representing elements of the Weyl algebra by labeled trees ⋮ Normal ordering \(q\)-bosons and combinatorics ⋮ Laguerre-type derivatives: Dobiński relations and combinatorial identities ⋮ Note on chromatic polynomials of the threshold graphs ⋮ Normal ordering problem and the extensions of the Stirling grammar ⋮ Path decompositions of digraphs and their applications to Weyl algebra

Cites Work

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• Bell numbers and coherent states
• Une théorie combinatoire des séries formelles
• Sequential quadratic programming methods for large-scale problems
• The general boson normal ordering problem
• Juggling and applications to \(q\)-analogues
• Boson normal ordering via substitutions and Sheffer-type polynomials
• Some useful combinatorial formulas for bosonic operators
• Normal ordering for deformed boson operators and operator-valued deformed Stirling numbers
• On the combinatorics of normal ordering bosonic operators and deformations of it
• Hierarchical Dobi ski-type relations via substitution and the moment problem

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